Exercicios Resolvidos — Probabilidade

3 face cards per suit × 4 suits = 12 face cards [ P = \frac1252 = \frac313 \approx 0.2308 ]

( \frac91216 ). Summary of Key Formulas Used | Concept | Formula | |---------|---------| | Classical probability | ( P(A) = \frac ) | | Conditional probability | ( P(A|B) = \fracP(A \cap B)P(B) ) | | Multiplication rule | ( P(A \cap B) = P(A)P(B|A) ) | | Bayes' theorem | ( P(A|B) = \fracP(BP(B) ) | | Binomial probability | ( P(X=k) = \binomnk p^k (1-p)^n-k ) | | Complement rule | ( P(A) = 1 - P(\neg A) ) | These exercises illustrate the most common reasoning patterns in introductory probability. Practice with variations (more dice, different decks, multiple events) to build intuition. probabilidade exercicios resolvidos

Red suits = hearts + diamonds → 2 suits × 3 face cards = 6 [ P = \frac652 = \frac326 \approx 0.1154 ] 3 face cards per suit × 4 suits

( \frac516 ). Exercise 6: Complement and "At Least One" Problem: If you roll a fair die 3 times, what is the probability of getting at least one 6? Solution: Easier to use complement: [ P(\textat least one 6) = 1 - P(\textno 6) ] Probability of no 6 in one roll = ( \frac56 ). [ P(\textno 6 in 3 rolls) = \left(\frac56\right)^3 = \frac125216 ] [ P(\textat least one 6) = 1 - \frac125216 = \frac91216 \approx 0.4213 ] Red suits = hearts + diamonds → 2

After removing 1 red, left: 3 red + 6 blue = 9 marbles. [ P(B_2 | R_1) = \frac69 = \frac23 ]

Favorable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes. [ P(\textsum = 7) = \frac636 = \frac16 \approx 0.1667 ]